On Kostant’s partition function

Dr. Pamela Harris
Associate Professor of Mathematics
Williams College

In this talk we recall that Kostant’s partition function counts the number of ways to represent a particular weight (vector) as a nonnegative integral sum of positive roots of a Lie algebra. We provide two fundamental uses for this function. The first is associated with the computation of weight multiplicities in finite-dimensional irreducible representations of classical Lie algebras and the second is in the computation of volumes of flow polytopes. We present some recent results in both of these areas including a connection to multiplex juggling and directions for future research.

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